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Quick detection of critical nodes has become a great concern to most investors and utilities recently due to its influence on prevention of the frequent occurrence of voltage collapse within a power network. This paper, therefore presents an option for detecting critical nodes, an approach which is based on the network topological characteristics of power networks. The mathematical formulations of the approach from the basic circuit theory laws were revisited. A Normalized Eigenvalue (NEV) index using eigenvalue and eigenvector analyses was then developed using MATLAB 2019b as the simulation tool. A simple 10-bus network was used to test the effectiveness of the NEV index method suggested in this paper. The NEV for all the network buses was determined and ranked in decreasing value of NEV to measure the criticality and vulnerability of each load node to voltage collapse within the system. Buses 6 had the highest value of NEV index (1.00) while bus 4 had the lowest NEV index (0.00) value. This suggested that there is a possibility of occurrence of over-voltage at bus 6 and undervoltage at bus 4. Therefore, buses 4 and 6 were identified as the critical buses, where placement of the reactive power support will be most beneficial. The results obtained were compared with those obtained using other methods documented in the literature. The comparison showed the effectiveness of the approach in quick identification of critical parts of the network most especially during critical outages.